A positive number and 5 more than it have product 204. What is the larger number?
Answer and explanation
Correct answer: 17
Let the positive number be x. The other number is x + 5, so the product condition gives x(x + 5) = 204. Thus x² + 5x − 204 = 0. Factoring gives (x + 17)(x − 12) = 0, so x = 12 or x = −17. Because the question specifies a positive number, x = 12 is valid. The larger number is therefore x + 5 = 17. A quick check gives 12 × 17 = 204, confirming the result. Option A is the smaller number, not the requested larger number; B and D do not form the stated pair with product 204. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
Let the positive number be x. The other number is x + 5, so the product condition gives x(x + 5) = 204. Thus x² + 5x − 204 = 0. Factoring gives (x + 17)(x − 12) = 0, so x = 12 or x = −17. Because the question specifies a positive number, x = 12 is valid. The larger number is therefore x + 5 = 17. A quick check gives 12 × 17 = 204, confirming the result. Option A is the smaller number, not the requested larger number; B and D do not form the stated pair with product 204. Therefore, option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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